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Spherical Bessel Function yn (G Dataflow)

Version:
    Last Modified: January 9, 2017

    Calculates the spherical Bessel function of the second kind.

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    x

    The input argument.

    Default: 0

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    n

    Order of the spherical Bessel function.

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    error in

    Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

    Default: No error

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    yn(x)

    Value of the spherical Bessel function of the second kind.

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    error out

    Error information. The node produces this output according to standard error behavior.

    Algorithm for Calculating the Spherical Bessel Function of the Second Kind

    For the spherical Bessel function of the second kind of order n, yn(x) is a solution to the following differential equation.

    x 2 d 2 w d x 2 + 2 x d w d x + ( x 2 n ( n + 1 ) ) w = 0

    The following equation shows the relationship of the spherical Bessel function of the second kind to the Bessel function of the second kind.

    y n ( x ) = π 2 x Y v ( x ) , v = n + 1 2

    The function is defined according to the following intervals for the input values.

    n , x [ 0 , )

    This node supports the entire domain of this function that produces real-valued results. For any integer value of order n, the function is defined for nonnegative real values of x.

    Where This Node Can Run:

    Desktop OS: Windows

    FPGA: Not supported


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